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Question:

 In Exercise, obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.

Answer:

Magnetic field strength, B = 6.5 × 10 - 4 T

Charge of the electron, e = 1.6 × 10 - 19 C

Mass of the electron, me = 9.1 × 10 - 31 kg

Velocity of the electron, v = 4.8 × 106 m/s

Radius of the orbit, r = 4.2 cm = 0.042 m

Frequency of revolution of the electron = v

Angular frequency of the electron = w = 2πv

Velocity of the electron is related to the angular frequency as:

v = rw

In the circular orbit, the magnetic force on the electron is balanced by the centripetal force. Hence, we can write:

This expression for frequency is independent of the speed of the electron.

On substituting the known values in this expression, we get the frequency as:

Hence, the frequency of the electron is around 18 MHz and is independent of the speed of the electron.


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